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NASA NTRS1973

Evaluation of LRC Spectral Analyses of Simulated Gust Velocity Data

The NASA Langley Research Center (LRC) has been computing power spectra of simulated atmospheric turbulence data by various techniques, in preparation for the B-57 gust velocity data analysis program. The results of these studies have confirmed earlier suspicions that conventional first-difference pre-whitening of gust velocity data can produce serious distortions in the spectral densities at very low frequencies (below the frequency of the gust velocity spectral "knee"). The results also indicate that the frequency averaging procedures have certain merits over ensemble averaging procedures in the computation of spectra by direct Fourier transform operations. Finally, the results do not reveal any significant difference in the spectral estimates obtained using Hann versus Parzen smoothing procedures.

Piersol, Allan G.↗
NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗
NASA NTRS1999

Large Eddy Simulation of a Forced Round Turbulent Buoyant Plume in Neutral Surroundings

Buoyant flows play an important role in various technological and environmental issues. For example, dispersal of pollutants, smoke, or volcano exhaust in the atmosphere, vertical motion of air, formation of clouds and other weather systems, and flows in cooling towers and fires are all determined primarily by buoyancy effects. The buoyancy force in such flows can originate from either a heat source or due to different densities between a fluid and its surroundings. Whatever the cause, the flow can be understood by studying the effects of the tight coupling between the thermal and the velocity fields since density differences can be characterized as temperature differences.

Basu, A. J.↗
NASA NTRS2004

Development of the Planar Inlet Design and Analysis Process (PINDAP)

The aerodynamic development of an engine inlet requires a comprehensive program of both wind tunnel testing and Computational Fluid Dynamics (CFD) simulations. To save time and resources, much "testing" is done using CFD before any design ever enters a wind tunnel. The focus of my project this summer is on CFD analysis tool development. In particular, I am working to further develop the capabilities of the Planar Inlet Design and Analysis Process (PINDAP). "PINDAP" is a collection of computational tools that allow for efficient and accurate design and analysis of the aerodynamics about and through inlets that can make use of a planar (two-dimensional or axisymmetric) geometric and flow assumption. PINDAP utilizes the WIND CFD flow solver, which is capable of simulating the turbulent, compressible flow field. My project this summer is a continuation of work that I performed for two previous summers. Two years ago, I used basic features of the PINDAP to design a Mach 5 hypersonic scramjet engine inlet and to demonstrate the feasibility of the PINDAP. The following summer, I worked to develop its geometry and grid generation capabilities to include subsonic and supersonic inlets, complete bodies and cowls, conic leading and trailing edges, as well as airfoils. These additions allowed for much more design flexibility when using the program.

Gruber, Christopher R.↗
NASA NTRS2006

Stirling Analysis Comparison of Commercial VS. High-Order Methods

The conclusions are: Low Reynold s number, wall bounded flow allows economical use of large eddy simulation for turbulent transition modeling. UHF and Compact comparable at conjugate heat transfer. UHF much better for turbulence modeling Modern methods much more efficient than those currently available commercially.

Dyson, Rodger W.↗
NASA NTRS2007

Minnowbrook I: 1993 Workshop on End-Stage Boundary Layer Transition

This volume contains materials presented at the Minnowbrook I-1993 Workshop on End-Stage Boundary Layer Transition, held at the Syracuse University Minnowbrook Conference Center, New York, from August 15 to 18, 1993. This volume was previously published as a Syracuse University report edited by John E. LaGraff. The workshop organizers were John E. LaGraff (Syracuse University), Terry V. Jones (Oxford University), and J. Paul Gostelow (University of Technology, Sydney). The workshop focused on physical understanding of the late stages of transition from laminar to turbulent flows, with the specific goal of contributing to improving engineering design of turbomachinery and wing airfoils. The workshop participants included academic researchers from the United States and abroad, and representatives from the gas-turbine industry and U.S. government laboratories. To improve interaction and discussions among the participants, no formal papers were required. The physical mechanisms discussed were related to natural and bypass transition, wake-induced transition, effects of freestream turbulence, turbulent spots, hairpin vortices, nonlinear instabilities and breakdown, instability wave interactions, intermittency, turbulence, numerical simulation and modeling of transition, heat transfer in boundary-layer transition, transition in separated flows, laminarization, transition in turbomachinery compressors and turbines, hypersonic boundary-layer transition, and other related topics. This volume contains abstracts and copies of the viewgraphs presented, organized according to the workshop sessions. The workshop summary and the plenary discussion transcript clearly outline future research needs.

LaGraff, John E.↗
NASA NTRS2009

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes - Part 1

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and efficiency are studied for six nominally second-order accurate schemes: a node-centered scheme, cell-centered node-averaging schemes with and without clipping, and cell-centered schemes with unweighted, weighted, and approximately mapped least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Results from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The second class of tests are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes are less accurate, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to the complexity of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping of the surface anisotropy or modifying the scheme stencil to reflect the direction of strong coupling.

Diskin, Boris↗
NASA NTRS2010

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Diskin, Boris↗
NASA NTRS2010

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom.

Diskin, Boris↗
NASA NTRS2003

Numerical Simulations of STOVL Hot Gas Ingestion in Ground Proximity Using a Multigrid Solution Procedure

A multi grid solution procedure for the numerical simulation of turbulent flows in complex geometries has been developed. A Full Multigrid-Full Approximation Scheme (FMG-FAS) is incorporated into the continuity and momentum equations, while the scalars are decoupled from the multi grid V-cycle. A standard kappa-Epsilon turbulence model with wall functions has been used to close the governing equations. The numerical solution is accomplished by solving for the Cartesian velocity components either with a traditional grid staggering arrangement or with a multiple velocity grid staggering arrangement. The two solution methodologies are evaluated for relative computational efficiency. The solution procedure with traditional staggering arrangement is subsequently applied to calculate the flow and temperature fields around a model Short Take-off and Vertical Landing (STOVL) aircraft hovering in ground proximity.

Wang, Gang↗
NASA NTRS2015

Parametric Design of Injectors for LDI-3 Combustors

Application of a partially calibrated National Combustion Code (NCC) for providing guidance in the design of the 3rd generation of the Lean-Direct Injection (LDI) multi-element combustion configuration (LDI-3) is summarized. NCC was used to perform non-reacting and two-phase reacting flow computations on several LDI-3 injector configurations in a single-element and a five-element injector array. All computations were performed with a consistent approach for mesh-generation, turbulence, spray simulations, ignition and chemical kinetics-modeling. Both qualitative and quantitative assessment of the computed flowfield characteristics of the several design options led to selection of an optimal injector LDI- 3 design that met all the requirements including effective area, aerodynamics and fuel-air mixing criteria. Computed LDI-3 emissions (namely, NOx, CO and UHC) will be compared with the prior generation LDI- 2 combustor experimental data at relevant engine cycle conditions.

injectors↗
NASA NTRS2016

Numerical Simulation of a Complete Low-Speed Wind Tunnel Circuit

A numerical simulation of the complete circuit of the NASA Langley 14 x 22-ft low-speed wind tunnel is described. Inside the circuit, all turning vanes are modeled as well as the five flow control vanes downstream of the 1st corner. The fan drive system is modeled using an actuator disk for the fan blades coupled with the fan nacelle. All the surfaces are modeled as viscous walls except the turning vanes, which were modeled as inviscid surfaces. NASA Langley's TetrUSS unstructured grid software was used for grid generation and flow simulation. Two turbulence models were employed in the present study, namely, the one-equation Spalart-Allmaras model and the shear stress transport (SST) model of Menter. The paper shows the flow characteristics in the circuit and compares the results with experimental data where available.

Nayani, Sudheer N.↗
NASA NTRS2018

High-Order Stabilized Finite Elements on Dynamic Meshes

The development of dynamic mesh capability for turbulent flow simulations using the Streamlined Upwind Petrov-Galerkin (SUPG) discretization is described. The current work extends previous research to include high-order spatial accuracy, including the satisfaction of the discrete geometric conservation law (GCL) on curved elements. Two closely-related schemes are described and the ability of these schemes to satisfy the GCL, while also maintaining temporal accuracy and conservation is assessed. Studies indicate that although one scheme discretizes the time derivative in conservative form, both schemes exhibit temporal conservation errors that decrease according to the expected design order of accuracy. The source of the temporal conservation errors is examined, and it is demonstrated that many finite-volume and finite-element schemes can also be expected to have difficulty strictly satisfying conservation in time. The effects on conservation are examined and, while present in the simulations, are seen to be negligible for the problems considered.

Anderson, W. Kyle↗
NASA NTRS2019

Scale-Resolving Simulations of Laminar-to-Turbulent Transition in Swept-Wing Flow

Aerodynamic shape optimization of swept Natural Laminar Flow (NLF) wing design plays an important role for the development of future energy-efficient commercial transport aircraft. Lack of predictive laminar-to-turbulent transition modeling capabilities is still limiting the extent to which design can rely on computational tools, while making costly wind tunnel and flight tests a necessity. Prediction of transition on practical 3D wing geometries using the e (sup N) method coupled with laminar boundary layer and linear stability codes or local statistical correlation CFD (Computational Fluid Dynamics) models such as the gamma - Re (sub theta) Langtry-Menter model have proven challenging, whereas transitional hybrid RANS-LES solvers have shown encouraging but still mitigated results.

Scale-resolving↗
NASA NTRS2019

Flight Performance Maneuver Planning for NASA’s X-57 “Maxwell” Flight Demonstrator – Part 1: Power-Off Glides

Distributed Electric Propulsion technology is expected to yield up to a fivefold increase in high-speed cruise efficiency for NASA’s X-57 “Maxwell” flight demonstrator when compared to a combustion-powered general aviation baseline. A portion of this increased efficiency is due to beneficial aero-propulsive interaction inherent to the distributed propulsion architecture. The measure of the relative increase in efficiency between a conventional and distributed propulsion wing will be extracted from comparisons between flight test data from the electrically powered X-57 Mod II configuration with a conventional wing, and from the electrically powered X-57 Mod III/IV configuration with a distributed propulsion wing. Flight test maneuvers that accommodate errors in instrumentation and the flight test environment are developed to establish the power-off drag characteristics for all X-57 configurations. Analysis of these maneuvers with typical errors, including pilot-in-the-loop simulation data that incorporates simulated atmospheric turbulence effects, shows that the proposed power-off flight maneuvers can generate accurate power-off drag predictions for the X-57. These predictions show that the power-off differences in aerodynamic performance between the conventional and distributed propulsion configurations can be accurately measured from flight test data in the presence of typical data error sources.

Borer, Nicholas K.↗